Shear viscosity of the normal phase of a unitary Fermi gas from theɛexpansion

Abstract

Using the $\ensuremath{\varepsilon}$-expansion technique, we compute $\ensuremath{\eta}/s$, where $\ensuremath{\eta}$ is the shear viscosity and $s$ is the entropy density of the normal phase of unitary Fermi gas in $d=4\ensuremath{-}\ensuremath{\varepsilon}$ dimensions to leading order (LO) in $\ensuremath{\varepsilon}$. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\ensuremath{\varepsilon}}^{2}$, which is LO. The LO result is temperature independent with $\ensuremath{\eta}/s\ensuremath{\simeq}(0.11/{\ensuremath{\varepsilon}}^{2})(\ensuremath{\hbar}/{k}_{B})$. The $d=3$ prediction for $\ensuremath{\eta}/s$ exceeds the $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{B}$ bound by a factor of about $1.4$.